Download Velocity

Regents Physics Review
#1
Vectors
Scalar
Magnitude(size) only
Vector
Magnitude(size) AND Direction
Distance
Displacement
Speed
Velocity
Mass
Weight
Work
Force
Momentum
Scalar is to vector as
(1) speed is to velocity
(2) displacement is to distance
(3) displacement is to velocity
(4) speed is to distance
What are the magnitudes of the
horizontal and vertical
components?
A model airplane heads due east at 1.50 meters per second, while the
wind blows due north at 0.70 meter per second. The scaled diagram
below represents these vector quantities.(June 2011)
66 Using a ruler, determine the scale used in the vector diagram. [1]
67 On the diagram above, use a protractor and a ruler to construct a vector to represent the
resultant velocity of the airplane. Label the vector R. [1]
68 Determine the magnitude of the resultant velocity. [1]
69 Determine the angle between north and the resultant velocity. [1]
A dog walks 8.0 meters due
north and then 6.0 meters due
east.
Using a metric ruler and the vector diagram, determine the scale used in the
diagram. [1]
On the diagram above, construct the resultant vector that represents the
dog’s total displacement. [1]
Determine the magnitude of the dog’s total displacement. [1]
Calculate the magnitude of the component of the 60.-newton force that is
parallel to the horizontal surface. [Show all work, including the equation and
substitution with units.] [2]
A baseball player runs 27.4 meters from the batter’s box to first base,
overruns first base by 3.0 meters, and then returns to first base.
Compared to the total distance traveled by the player, the magnitude of
the player’s total displacement from the batter’s box is
(1) 3.0 m shorter (2) 6.0 m shorter (3) 3.0 m longer (4) 6.0 m longer
A child walks 5.0 meters north, then 4.0 meters east, and finally 2.0
meters south. What is the magnitude of the resultant displacement of the
child after the entire walk?
(1) 1.0 m
(2) 5.0 m
(3) 3.0 m
(4) 11.0 m
As the angle between two concurrent forces decreases, the magnitude of the
force required to produce equilibrium
(1) decreases
(2) increases
(3) remains the same
Which is a vector quantity?
(1) speed
(2) work
(3) mass
(4) displacement
A soccer player kicks a ball with an initial velocity of 10. meters per second at an
angle of 30.° above the horizontal. The magnitude of the horizontal component
of the ball’s initial velocity is
(1) 5.0 m/s
(2) 8.7 m/s
(3) 9.8 m/s
(4) 10. m/s
Regents Physics Review
#2
Motion,
Acceleration
(SeeVelocity,
Review Book
P. 10-17)
Velocity is the change in displacement per unit time.
Velocity is a vector, it must include a direction such as
+,-, left, right, up, down, north, south, etc.
Speed is simply the change in distance over time
regardless of direction. Speed is a scalar.
Uniform Velocity = constant velocity; not changing.
Average Velocity = Total displacement / Total time
Acceleration = change in velocity over time.
Acceleration is a vector.
Equations from
Reference Tables:
Distance
Distance vs. Time graphs
Slope = velocity
Time
Straight line = constant velocity
= NOT accelerating
Distance
Distance vs. Time graphs
Slope = velocity = 0
Time
Straight HORIZONTAL line = 0 velocity
= NOT moving
Distance
Distance vs. Time graphs
Slope = velocity
Time
Curved line = changing velocity = acceleration
Velocity
Velocity vs. Time graphs
Slope = acceleration
Time
Straight line = uniform acceleration (e.g. gravity)
A 25-newton weight falls freely from rest from the
roof of a building. What is the total distance the
weight falls in the first 1.0 second?
(1) 19.6 m
(2) 9.8 m
(3) 4.9 m
(4) 2.5 m
If a car accelerates uniformly from rest to 15
meters per second over a distance of 100. meters,
the magnitude of the car’s acceleration is
(1) 0.15 m/s2 (2) 1.1 m/s2 (3) 2.3 m/s2 (4) 6.7 m/s2
Projectile Motion
When you throw an object into the air (projectile):
1. The X component of the velocity is constant (does not change)
2. The Y component of the velocity starts out large, slows down to 0,
then increases back to where it started.
3. What goes up, must come down…in the same amount of time. This
statement means that if it takes 4 seconds for an object to hit the ground
after it is thrown, then the object must have taken 2 seconds to get to the
top and 2 seconds to get back to the ground.
Vy= 0
Vy
Vx
Vy
Vx
Vx
Vy
Vx
Vy
Vx
V
Θ
Vx = Vcos Θ
Vy = Vsin Θ
Summary
For projectile motion, remember the following:
1. Time up = Time down.
2. The projectile reaches its highest point midway through its
flight. (half the time & half the horizontal distance)
3. At the highest point, the vertical velocity = 0 m/s
4. Gravity affects only the vertical velocity.
5. The horizontal velocity is constant. (stays the same)
6. The shape of the path is a parabola.
The diagram below represents a ball being kicked by a foot and rising at an
angle of 30.0 from the horizontal. The ball has an initial velocity of 5.0
meters per second. [Neglect friction.]
A. What is the magnitude of the horizontal component of the ball's initial
velocity?
(1) 2.5 m/s
(2) 4.3 m/s
(3) 5.0 m/s
(4) 8.7 m/s
B. As the ball rises, the vertical component of its velocity
(I) decreases
(2) increases
(3) remains the same
A rocket is launched at an angle of 60° to the horizontal.
The initial velocity of the rocket is 500 meters per
second. [Neglect friction.]
A. The vertical component of the initial velocity is
(1) 250 m/s (2) 433 m/s (3) 500 m/s (4) 1000 m/s
B. Compared to the horizontal component of the rocket's
initial velocity, the horizontal component after 10
seconds would be
(1) less
(2) greater
(3) the same
Time to “A” = 0.50 s
Time to “B” = 1.00 s
60 Determine the magnitude of the horizontal component of the velocity of the car
at point B. [Neglect friction.] [1]
61 Determine the magnitude of the vertical velocity of the car at point A. [1]
62 Calculate the magnitude of the vertical displacement, dy, of the car from point A
to point B. [Neglect friction.] [Show all work, including the equation and substitution
with units.] [2]
11 A ball is thrown vertically upward with an initial
velocity of 29.4 meters per second. What is the
maximum height reached by the ball? [Neglect friction.]
(1) 14.7 m
(2) 29.4 m
(3) 44.1 m
(4) 88.1 m
Regents Physics Review
#3
Newton’s Laws, Forces, Friction
(See Review Book P.22-33)
Newton’s First Law of Motion: The Law of Inertia
An object will resist any change in its state of motion.
An object at rest will stay at rest; an object in motion will stay moving in a
straight line at a constant speed unless acted on by an unbalanced force.
Mass is the measure of an object’s inertia.
Newton’s Second Law of Motion: Force, Mass, and Acceleration
An unbalanced force causes an object to accelerate: F = ma
Equilibrium: All forces are balanced.
Newton’s Third Law of Motion: Action and Reaction
For every force there is an equal force in the opposite direction.
Newton’s Law of Universal Gravitation: All matter attracts other matter.
Fg = G m1 m2 / r2
Weight is a force caused by gravity:
F = ma
F = mg
On Earth, g = 9.81 m/s2
Friction is a force that opposes the motion of an
object and depends upon the type of surfaces that
are in contact with each other.
Friction can be:
“sliding” or “rolling”
“static” or “kinetic”
Each surface has its own coefficient of friction.
An object on an inclined plane has several forces acting upon it:
Weight, Normal Force, Force parallel to the plane, and Friction.
2.
1.
3.
4.
1.
2.
3.
4.
Force parallel to plane
Friction
Normal Force (perpendicular to plane
Weight
Centripetal Force
Inertia tends to keep the object in a straight line.
Centripetal Force: Force toward the center of a circle.
The result is circular motion.
Inertia
Centripetal
Force
12 The diagram below represents a mass, m, being swung clockwise at
constant speed in a horizontal circle.
At the instant shown, the centripetal force acting on mass m is directed
toward point
(1) A
(2) B
(3) C (4) D
7 The magnitude of the centripetal force acting on an object traveling in a
horizontal, circular path will decrease if the
(1) radius of the path is increased (3) direction of motion of the object is reversed
(2) mass of the object is increased (4) speed of the object is increased
8 The centripetal force acting on the space shuttle as it orbits Earth is equal to the
shuttle’s
(1) inertia
(2) momentum
(3) velocity
(4) weight
A student and the waxed skis he is wearing have a combined weight of 850
newtons. The skier travels down a snow--covered hill and then glides to the
east across a snow-covered, horizontal surface.
53 Determine the magnitude of the normal force exerted by the snow on the
skis as the skier glides across the horizontal surface. [1]
54–55 Calculate the magnitude of the force of friction acting on the skis as the
skier glides across the snow-covered, horizontal surface. [Show all work,
including the equation and substitution with units.] [2]
70–71 Calculate the elongation of the spring produced by the suspended 2.00kilogram mass. [Show all work, including the equation and substitution with
units.] [2]
72–73 Calculate the total elastic potential energy stored in the spring due to the
suspended 2.00-kilogram mass. [Show all work, including the equation and
substitution with units.] [2]
13 As shown in the diagram below, an open box and its contents have a combined
mass of 5.0 kilograms. A horizontal force of 15 newtons is required to push the box
at a constant speed of 1.5 meters per second across a level surface.
The inertia of the box and its contents increases if there is an increase in the
(1) speed of the box
(2) mass of the contents of the box
(3) magnitude of the horizontal force applied to the box
(4) coefficient of kinetic friction between the box and the level surface
Regents Physics Review
#4
Momentum, Energy
Work, Power
Momentum: Mass x Velocity
Momentum is a vector quantity because velocity is a vector.
Formula:
p = mv
Law of Conservation of Momentum: Total momentum of a system is conserved…all
the “pieces” of momentum must be accounted for and add up to the total you started
with.
Total Momentum before a collision = Total Momentum after a collision
Impulse = Force x time
J = Ft
Impulse = change of momentum: Ft = mv
Energy is the capacity to do work.
Potential= “stored up”
Kinetic = moving
Work = a change in energy (potential or kinetic)
Work = force x distance.
Work can only be done if the force is in the same direction as the direction of motion!
Power = work / time or “How fast you do work.”
The diagram below represents two masses before and after they collide. Before
the collision, mass mA is moving to the right with speed v, and mass mB is at rest.
Upon collision, the two masses stick together.
Write an expression for V’ (the velocity after the collision.)
A 0.149-kilogram baseball, initially moving at 15 meters per second, is brought
to rest in 0.040 second by a baseball glove on a catcher’s hand. The magnitude
of the average force exerted on the ball by the glove is
(1) 2.2 N
(2) 2.9 N
(3) 17 N (4) 56 N
A 3.1-kilogram gun initially at rest is free to move. When a 0.015-kilogram
bullet leaves the gun with a speed of 500. meters per second, what is the
speed of the gun?
(1) 0.0 m/s
(2) 2.4 m/s
(3) 7.5 m/s
(4) 500. m/s
A bicycle and its rider have a combined mass of 80. kilograms and a speed of 6.0
meters per second. What is the magnitude of the average force needed to bring the
bicycle and its rider to a stop in 4.0 seconds?
(1) 1.2 x102 N
(2) 3.2 x102 N
(3) 4.8 x102 N
(4) 1.9 x103 N
Calculate the magnitude of the impulse applied to a 0.75-kilogram cart to
change its velocity from 0.50 meter per second east to 2.00 meters per second
east. [Show all work, including the equation and substitution with units.] [2]
Which statement describes the kinetic energy and total mechanical energy of a block
as it is pulled at constant speed up an incline?
(1) Kinetic energy decreases and total mechanical energy increases.
(2) Kinetic energy decreases and total mechanical energy remains the same.
(3) Kinetic energy remains the same and total mechanical energy increases.
(4) Kinetic energy remains the same and total mechanical energy remains the same.
Calculate the kinetic energy of a particle with a mass of 3.34 × 10-27 kilogram
and a speed of 2.89 × 105 meters per second. [Show all work, including the
equation and substitution with units.] [2]
Which graph represents the relationship between the gravitational potential energy
(GPE) of an object near the surface of Earth and its height above the surface of
Earth?
A ball is dropped from the top of a cliff. Which graph best represents the
relationship between the ball’s total energy and elapsed time as the ball falls to
the ground? [Neglect friction.]
A 1200-kilogram car moving at 12 meters per second collides with a 2300kilogram car that is waiting at rest at a traffic light. After the collision, the cars lock
together and slide. Eventually, the combined cars are brought to rest by a force of
kinetic friction as the rubber tires slide across the dry, level, asphalt road surface.
Calculate the speed of the locked-together cars immediately after the collision.
[Show all work, including the equation and substitution with units.] [2]
Calculate the magnitude of the frictional force that brings the locked-together cars
to rest. [Show all work, including the equation and substitution with units.] [2]
The diagram below shows a toy cart possessing 16 joules of kinetic energy
traveling on a frictionless, horizontal surface toward a horizontal spring.
If the cart comes to rest after compressing the spring a distance of 1.0 meter,
what is the spring constant of the spring?
(1) 32 N/m
(2) 16 N/m
(3) 8.0 N/m
(4) 4.0 N/m
The diagram below represents a 155-newton box on a ramp. Applied force F causes
the box to slide from point A to point B.
What is the total amount of gravitational potential energy gained by the box?
(1) 28.4 J
(2) 279 J
(3) 868 J
(4) 2740 J
A vertically hung spring has a spring constant of 150. newtons per meter. A
2.00-kilogram mass is suspended from the spring and allowed to come to rest.
Calculate the elongation of the spring produced by the suspended 2.00-kilogram
mass. [Show all work, including the equation and substitution with units.] [2]
Calculate the total elastic potential energy stored in the spring due to the
suspended 2.00-kilogram mass. [Show all work, including the equation and
substitution with units.] [2]
Regents Physics Review
#5
Waves
Waves
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Transverse Wave
Longitudinal (Compression) Wave
Standing waves
Velocity = Frequency x Wavelength
Superposition, Phase
Reflection
Refraction
Normal
“Bend toward the Normal,” “Bend awwy from the Normal”
Diffraction
Polarization
Angle of Incidence = Angle of Reflection
Angle of Refraction
Index of Refraction
Spectrum
Transverse Wave (Electromagnetic,Light)
Wavelength
Crest or Peak
Valley or Trough
Longitudinal or Compression Wave (Sound)
Compression
“squeezed together”
Rarefaction
Wavelength
“spread apart”
Standing Wave
Node
Antinode
What is the total number of nodes and antinodes in the
standing wave?
(1) 3 nodes and 2 antinodes
(2) 2 nodes and 3 antinodes
(3) 5 nodes and 4 antinodes
(4) 4 nodes and 5 antinodes
What is the wavelength of this standing wave?
(1) 2.15 m
(2) 4.30 m
(3) 6.45 m
(4) 8.60 m
The superposition of the waves produces the greatest positive displacement of
the medium from its rest
position at point
(1) A
(2) B
(3) C
(4) D
Reflection
The angle of reflection for the light ray is
(1) 25°
(2) 35°
(3) 50.°
(4) 65°
Refraction
Diffraction: “Bending” around corners.
69 Measure the angle of incidence for the light ray to the nearest degree. [1]
70 Calculate the angle of refraction of the light ray when it enters the Lucite
block. [Show all work, including the equation and substitution with units.] [2]
71 What is the angle of refraction of the light ray as it emerges from the Lucite
block back into air? [1]
65 A wave generator having a constant frequency produces parallel wave fronts in
a tank of water of two different depths. The diagram below represents the wave
fronts in the deep water. As the wave travels from the deep water into the shallow
water, the speed of the waves decreases.
On the diagram below, use a straightedge to draw at least three lines to represent
the wave fronts, with appropriate spacing, in the shallow water. [1]
Slows down
Shorter Wavelength
Same Frequency
(Slows down, shorter wavelength)
55 A periodic wave travels at speed v through medium A. The wave passes
with all its energy into medium B. The speed of the wave through medium B
is v/2 . On the diagram below, draw the wave as it travels through
medium B. [Show at least one full wave.] [1]
Base your answers to questions 72 through 74 on the information and diagram
below. A ray of monochromatic light having a frequency of 5.09 × 1014 hertz is
incident on an interface of air and corn oil at an angle of 35° as shown. The ray is
transmitted through parallel layers of corn oil and glycerol and is then reflected from
the surface of a plane mirror, located below and parallel to the glycerol layer. The
ray then emerges from the corn oil back into the air at point P.
72 Calculate the angle of refraction of the light ray as it enters the corn oil from air.
[Show all work, including the equation and the substitution with units.] [2]
73 Explain why the ray does not bend at the corn oil-glycerol interface. [1]
74 On the diagram above, use a protractor and straightedge to construct the
refracted ray representing the light emerging at point P into air. [1]
Regents Physics Review
#6
Electricity & Magnetism
Vocabulary and Terms
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Charge
Like Poles or Charges, Unlike Poles or Charges
Electric Field
Electrostatic Force
Potential Difference = Voltage = V
Current = amperage = I
Resistance = Ohms = R symbol = Ω
Ohm’s Law: V = IR R = V/I I = V/R
Resistivity: ρ (rho)
Series Circuit
Parallel Circuit
Power
Energy (Work)
Deflects toward opposite charge.
North
Negative
South
Positive
Magnetic Field
Like Poles Repel
On the diagram below, draw at least four electric field lines in the region
between the two positively charged particles. [1]
Series Circuit: Current is constant, Voltage adds up, Resistance adds up.
Parallel Circuit: Voltage is constant, Current adds up, 1/Req = 1/R1+1/R2 +…
23 Which circuit has the smallest equivalent resistance?
Base your answers to questions 59 and 60 on the information and diagram
below. A 10.0-meter length of copper wire is at 20°C. The radius of the wire
is 1.0 × 10–3 meter.
59 Determine the cross-sectional area of the wire. [1]
60 Calculate the resistance of the wire. [Show all work, including the equation
and substitution with units.] [2]
Regents Physics Review
#7
Modern Physics
Dual Nature of Light: Particle and Wave
Photon: Particle of light
Strong Force: Force holding nucleus (protons and neutrons) together
Weak Force: Force between electrons and the nucleus
Photoelectric Effect: Light can cause electrons to be emitted from matter.
Quarks: Up, Down, Top, Bottom, Charm, Strange
Bohr Model: Atoms seen like the solar system
Rutherford Experiment: Atom is mostly empty space with a solid nucleus.
Energy Levels
Planck’s Constant
The Atom
J.J.Thomson: “Plum Pudding” Model
Rutherford: Gold Foil Experiment…
empty space and nucleus
Alpha(+)
+
Bohr: Planetary Model
Energy Levels
Quarksavers
6 Flavors
Up
Top
Charm
Down
Bottom
Strange